In the present paper a new semantic framework for modelling the distinction between implicit and explicit belief is proposed and contrasted with the currently standard framework based on the idea that explicit belief can be construed as implicit belief accompanied by awareness. It is argued that within this new framework it is possible to get both a more intuitive interpretation of the aforementioned distinction and a straightforward solution to two critical problems to which the standard view is subjected. A system (...) of logic for belief is introduced and proved to be complete with respect to the class of all frames for implicit and explicit belief constructed in accord to the new view. (shrink)

This paper outlines a formal account of tensed sentences that is consistent with Ockhamism, a view according to which future contingents are either true or false. The account outlined substantively differs from the attempts that have been made so far to provide a formal apparatus for such a view in terms of some expressly modified version of branching time semantics. The system on which it is based is the simplest quantified modal logic.

In this article, the relationship between second-order comprehension and unrestricted mereological fusion (over atoms) is clariﬁed. An extension PAF of Peano arithmetic with a new binary mereological notion of “fusion”, and a scheme of unrestricted fusion, is introduced. It is shown that PAF interprets full second-order arithmetic, Z_2.

In the paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no longer (...) play a distinctive role. This account employs a new notion of semantic constraints. The paper includes some preliminary definitions and results in the new framework. (shrink)

Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Omega-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren's development of Nonstandard Analysis inside constructive mathematics.